72.5.36 problem 37 (v)

Internal problem ID [14722]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.6 page 89
Problem number : 37 (v)
Date solved : Tuesday, January 28, 2025 at 07:12:43 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\cos \left (\frac {\pi y}{2}\right ) \end{align*}

✓ Solution by Maple

Time used: 0.086 (sec). Leaf size: 48

dsolve(diff(y(t),t)=cos(Pi/2*y(t)),y(t), singsol=all)
 

\[ y = \frac {2 \arctan \left (\frac {{\mathrm e}^{\pi \left (t +c_{1} \right )}-1}{{\mathrm e}^{\pi \left (t +c_{1} \right )}+1}, \frac {2 \,{\mathrm e}^{\frac {\pi \left (t +c_{1} \right )}{2}}}{{\mathrm e}^{\pi \left (t +c_{1} \right )}+1}\right )}{\pi } \]

✓ Solution by Mathematica

Time used: 0.458 (sec). Leaf size: 31

DSolve[D[y[t],t]==Cos[Pi/2*y[t]],y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to \frac {2 \arcsin \left (\coth \left (\frac {1}{2} \pi (t+c_1)\right )\right )}{\pi } \\ y(t)\to -1 \\ y(t)\to 1 \\ \end{align*}